Most power systems today are run using two or more wires alternating current (AC) at low, medium and high voltages and in some cases using high voltage direct current (DC) (HVDC).
Both AC and DC transmission lines have losses which are proportional to the square of current and the resistance of the wires (i.e. I2R). The power transmitted is proportional to the product of the current and the voltage if they are in phase.
In order to reduce the transmission losses, the voltages are increased in the case of AC using transformers and in the case of DC power electronic converters and transformers. The most efficient way of transmitting power in a two wire single generator system is when the current is in phase with the generator voltage. In the case of multiple wires and generators, the way of transmitting currents with minimum losses becomes more complex to resolve.
Power networks may be small networks or micro-grids or large national grids with loads and supplies of many different forms.
Generally power systems are made up of: generators which transfer energy from a source of heat, light, wind, chemical or other energy into electrical energy; transmission networks which transport energy over long distances to distribution networks; distribution networks which distribute energy to loads; and the loads which absorb energy at a random basis in a finite domain.
New innovations in power electronics have provided new ways to optimise power systems by reducing power losses. The new developments have also led to opportunities for private customers to generate power from wind or sun energy and inject power into the grid as well as supplying reactive power for the load to reduce current magnitude drawn from the grid which otherwise increases transmission losses.
Due to advancing technology, it is becoming easier and more economical to generate power at various points of interest on a network including at the point of consumption. This power is not only used to supply loads at the point of consumption, but also to be injected into the power network when excess power is generated. Injecting power into the network can be done in many different ways as modem power electronic converters can easily control the magnitude and phase angle of the currents that are injected into each of the wires of the network. This therefore raises the question as to what these need to be so that the network will receive or supply power with minimum transmission losses.
The power in a multi-wire system is normally injected into a network equally in magnitude and in phase with the voltage at the point of connection. However, this is not necessarily the most efficient way for power to flow to its point of consumption as the resistance and reactance characteristics as well as the voltage of each wire may not always be the same.